2 Answers
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Unfortunately, no physically reasonable detector could ever detect gravitons. For example, a detector with the mass of Jupiter placed in close orbit around a neutron star would only be expected to observe one graviton every 10 years (see the below paper). The few that would be detected would be indistinguishable from the background 'noise', i.e. neutrinos.

Even though we can't detect individual gravitons, gravitational wave detectors may shed some light on them, since the graviton is the quantum of the gravitational wave (similar to how early 20th century physicists studied the nature of the photon based on properties of light, such as the photoelectric effect.).

Does not detection of gravitational waves actually amount to detection of gravitons?
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AnixxAug 13 '12 at 22:58

@Annix In my answer, I was referring to direct detection of gravitons. Of course, you may argue that since quantum mechanics requires waves to have quanta with energy proportional to their frequencies (Planck's law, $E = hf$), and since gravitational waves exist, then so must gravitons.
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Mark MAug 13 '12 at 23:01

To me the possibility of detection is highly dependent on graviton's energy. Possibly natural gravitons are difficult to detect but given a source of high-energy gravitons, they would not be that difficult to detect.
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AnixxAug 13 '12 at 23:06